Formally, we define \((v_{n}, a_{n})\)  as the encoded visual and audio representations of the \(n\) -th video, i.e\(v_{n}=f_v(x_n)\) , \(a_{n}=f_a(x_n)\) .
A general paradigm is to detect synchronized pair of \((v\) , \(a)\)  in a contrastive manner.
When \(v\)  and \(a\)  are from the same location of one video, they are synchronized and identified as positive sample pair.
When they are from different videos, they form a negative pair.
By sampling massive positive and negative visual-audio pairs, the noise-contrastive loss [1]}, [2]} can be formulated as:
\(\mathcal {L}_{nce}(v,a) = - \frac{1}{N}\sum _{n=1}^{N}log \frac{sim(v_{n},a_{n})}{\sum _{m}sim(v_{n},a_{m})},\) 
